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The arrows at either end of the line indicate that the number line extends forever in each direction. There is no greatest positive number and there is no smallest negative number    .

Doing the Manipulative Mathematics activity "Number Line-part 2" will help you develop a better understanding of integers.

Plot the numbers on a number line:

  1. 3
  2. −3
  3. −2

Solution

Draw a number line. Mark 0 in the center and label several units to the left and right.

  1. ⓐ To plot 3 , start at 0 and count three units to the right. Place a point as shown in [link] .
    This figure is a number line scaled from negative 4 to 4, with the point 3 labeled with a dot.
  2. ⓑ To plot −3 , start at 0 and count three units to the left. Place a point as shown in [link] .
    This figure is a number line scaled from negative 4 to 4, with the point negative 3 labeled with a dot.
  3. ⓒ To plot −2 , start at 0 and count two units to the left. Place a point as shown in [link] .
    This figure is a number line scaled from negative 4 to 4, with the point negative 2 labeled with a dot.

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Plot the numbers on a number line.

  1. 1
  2. −1
  3. −4


This figure is a number line. The point negative 4 is labeled with the letter c, the point negative 1 is labeled with the letter b, and the point 1 is labeled with the letter a.

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Plot the numbers on a number line.

  1. −4
  2. 4
  3. −1


This figure is a number line. The point negative 4 is labeled with the letter a, the point negative 1 is labeled with the letter c, and the point 4 is labeled with the letter b.

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Order positive and negative numbers

We can use the number line    to compare and order positive and negative numbers. Going from left to right, numbers increase in value. Going from right to left, numbers decrease in value. See [link] .

This figure is a number line. Above the number line there is an arrow pointing to the right labeled increasing. Below the number line there is an arrow pointing to the left labeled decreasing.

Just as we did with positive numbers, we can use inequality symbols to show the ordering of positive and negative numbers . Remember that we use the notation a < b (read a is less than b ) when a is to the left of b on the number line. We write a > b (read a is greater than b ) when a is to the right of b on the number line. This is shown for the numbers 3 and 5 in [link] .

This figure is a number line with points 3 and 5 labeled with dots. Below the number line is the statements 3 is less than 5 and 5 is greater than 3.
The number 3 is to the left of 5 on the number line. So 3 is less than 5 , and 5 is greater than 3 .

The numbers lines to follow show a few more examples.


This figure is a number line with points 1 and 4 labeled with dots.

4 is to the right of 1 on the number line, so 4 > 1 .

1 is to the left of 4 on the number line, so 1 < 4 .


This figure is a number line with points negative 2 and 1 labeled with dots.

−2 is to the left of 1 on the number line, so −2 < 1 .

1 is to the right of −2 on the number line, so 1 > −2 .


This figure is a number line with points negative 3 and negative 1 labeled with dots.

−1 is to the right of −3 on the number line, so −1 > −3 .

−3 is to the left of −1 on the number line, so −3 < 1 .

Order each of the following pairs of numbers using < or >:

  1. 14 ___ 6
  2. −1 ___ 9
  3. −1 ___ −4
  4. 2 ___ −20

Solution

Begin by plotting the numbers on a number line as shown in [link] .

This figure is a number line with points negative 20, negative 4, negative 1, 2, 6, 9, and 14 labeled with dots.

Compare 14 and 6. 14 ___ 6
14 is to the right of 6 on the number line. 14 > 6
Compare −1 and 9. −1 ___ 9
−1 is to the left of 9 on the number line. −1 < 9
Compare −1 and −4. −1 ___ −4
−1 is to the right of −4 on the number line. −1 > −4
Compare 2 and −20. −2 ___ −20
2 is to the right of −20 on the number line. 2 > −20
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Order each of the following pairs of numbers using < or >.

  1. 15 ___ 7
  2. −2 ___ 5
  3. −3 ___ −7
  4. 5 ___ −17

  1. >
  2. <
  3. >
  4. >

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Order each of the following pairs of numbers using < or >.

  1. 8 ___ 13
  2. 3 ___ −4
  3. −5 ___ −2
  4. 9 ___ −21

  1. <
  2. >
  3. <
  4. >

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Find opposites

On the number line, the negative numbers are a mirror image of the positive numbers with zero in the middle. Because the numbers 2 and −2 are the same distance from zero, they are called opposites    . The opposite of 2 is −2 , and the opposite of −2 is 2 as shown in [link] (a). Similarly, 3 and −3 are opposites as shown in [link] (b).

This figure shows two number lines. The first has points negative 2 and positive 2 labeled. Below the first line the statement is the numbers negative 2 and 2 are opposites. The second number line has the points negative 3 and 3 labeled. Below the number line is the statement negative 3 and 3 are opposites.

Opposite

The opposite of a number is the number that is the same distance from zero on the number line, but on the opposite side of zero.

Find the opposite of each number:

  1. 7
  2. −10

Solution

  1. The number −7 is the same distance from 0 as 7 , but on the opposite side of 0 . So −7 is the opposite of 7 as shown in [link] .
    This figure is a number line. The points negative 7 and 7 are labeled. Above the line it is shown the distance from 0 to negative 7 and the distance from 0 to 7 are both 7.
  2. The number 10 is the same distance from 0 as −10 , but on the opposite side of 0 . So 10 is the opposite of −10 as shown in [link] .
    This figure is a number line. The points negative 10 and 10 are labeled. Above the line it is shown the distance from 0 to negative 10 and the distance from 0 to 10 are both 10.

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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